Question

Suppose you have 14 tubes of paint. How many distinct color groupings can you make with your paint?

Answer 1

Given:

`n=14`

The total possibilities that can be made is the complete set and subsets.

Hence,

`\begin{gathered} N=2^n \\ N=2^(14) \\ N=16384 \end{gathered}`

But empty set will not be there in the distinct color groupings.

Thus,

`\begin{gathered} N=16384-1 \\ N=16,383 \end{gathered}`

Therefore, there are 16,383 distinct color groupings that can be made.